Question: What is the extraneous solution to these equations? $\dfrac{x^2 - 22}{x - 1} = \dfrac{3}{x - 1}$
Multiply both sides by $x - 1$ $ \dfrac{x^2 - 22}{x - 1} (x - 1) = \dfrac{3}{x - 1} (x - 1)$ $ x^2 - 22 = 3$ Subtract $3$ from both sides: $ x^2 - 22 - (3) = 3 - (3)$ $ x^2 - 22 - 3 = 0$ $ x^2 - 25 = 0$ Factor the expression: $ (x + 5)(x - 5) = 0$ Therefore $x = -5$ or $x = 5$ The original expression is defined at $x = -5$ and $x = 5$, so there are no extraneous solutions.